A Critique of Factor Analysis of Interest Rates

Abstract

Term structure models typically attempt to explain the full range of observed fluctuation in the yield curve with a small number of independent factors. Factor analysis, a common tool in this effort, generally shows that three factors capture a large proportion of the variation in the curve. The first (most important) factor applies across all maturities and reflects the level of yields; the second affects the slope of the yield curve; and the third relates to its curvature. In this article, Lekkos argues that much of the apparent explanatory power of this factor structure may be an artifact induced by the arbitrage relationship that requires a given spot rate to equal the average of the forward rates over that maturity. Factor analysis on spot rates in four major countries shows that three factors explain about 97% of the variance in each case, but the fit with forward rates is distinctly less good. Lekkos then demonstrates that even in a simulated economy with completely independent forward rates, as long as spot rates are arbitrage-free and equal to averages of the relevant forward rates, standard factor analysis produces a factor structure that explains over 90% of overall yield variation, and loadings on the individual factors that closely resemble the patterns found for the actual markets.